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Index/Classical mechanics/CLS-28

CLS-28

Reduced mass

Two-body reduction.

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GoverningReduced mass

Governing equation

μ=m1m2/(m1+m2)\mu=m_1 m_2/(m_1+m_2)

where

m1
m1 (kg)
m2
m2 (kg)
mu
Reduced mass (kg)

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-28 — Reduced mass) is the form associated with Reduced mass. Working symbols: m1m1, m2m2 →\rightarrow mumu. Two-body reduction. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute mumu from m1m1, m2m2 in Classical mechanics via μ=m1m2/(m1+m2)\mu=m_1 m_2/(m_1+m_2) Two-body reduction. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given m1=4.000 kgm1 = 4.000\,\mathrm{kg}, m2=6.000 kgm2 = 6.000\,\mathrm{kg}, the governing relation μ=m1m2/(m1+m2)\mu=m_1 m_2/(m_1+m_2) yields mu=2.400 kgmu = 2.400\,\mathrm{kg}. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Reduced mass mu2.400 kg
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CLS-28 · orbit
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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Two-body reduction. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube